204 ON THE CONDUCTION OF HEAT IN CRYSTALS.
symmetry, and similarly in other cases. When the plate was not perpendicular to an axis of thermic symmetry, the circumstance was indicated by the non-correspondence of the ovals formed on the opposite faces, the line joining the centres of the ovals being in that case oblique to the faces.
The subject of crystalline conduction had previously been investigated theoretically by M. Duhamel, in a memoir presented to the Academy of Sciences in 1828, and printed in the 21st Oakier of the Journal de rfJcole I^olytechniyue, p. 356. In this memoir the author deduces the general expressions for the flux of heat, and the equation of motion of heat, from the hypothesis of molecular radiation, and applies the general equations to the solution of a few simple problems, or at least problems which may very simply be reduced to the corresponding problems relating to uncrysiallized media. After the, publication of the researches of M. de Senannont, M. Duhamel was induced to resume the subject, and in a memoir printed in the 32nd (JdJiler of the above-mentioned Junrnul, he has deduced from theory a number of general consequences which are directly ap-plicnble to the. experiments of M. de Senannont.
In the following paper, I propose, to present the theory of crystalline conduction in a, form independent, of the hypothesis of molecular radiation- a hypothesis which for my own part I regard as very questionable. The subject will thus be consider-ably simplified, for in fact the results {low readily from certain very general assumed laws, which no doubt follow as consequences of the hypothesis of molecular radiation, but which are of such simplicity that, they would seem to follow from almost any rea-sonable hypothesis relating to the manner in which the passage of heat takes place in the interior of a solid body. As regards the mathematical deduction of consequences from the general formula-, I have introduced the consideration of what may be called an ansilinry ,sW/V/, by which means problems relating to crystallised bodies arc reduced to corresponding problems relating to ordinary media. All the principal results of M. Duhamel, of which one at least- was obtained by him in a very artificial manner, are thus rendered almost self-evident, or else directly reduced to known results relating to ordinary media; and some results of still greater generality follow with equal facility.